Apple-ID/icloud/Mail login-fails stating "is already signed in to iCloud"

MacBook Pro, Catalina, MacOs 10.15

I signed-out from iCloud on my MacBook Pro and wanted to sign-in again.

On my MacBook Pro

I went to: "Apple"-->System Preferences-->AppleID

I typed my apple-ID and my password

error message: "XYZ@icloud.com is already signed in to iCloud."

"To use this Apple ID as your primary iCloud account, delete it from Internet Accounts and sign in again."

I checked "internet accounts" and cleared the account on the list (which was my second email account from a different provider, which on my Mac is not linked to "mail", but in my iPhone, both, my iCloud.com and the other are linked to "Mail")

I tried again (after restart of computer)

Still, I receive the same error message.

I removed the MacBook Pro from "devices" on my iPhone (app-ID --> devices)

I signed-out my iPhone (15pro, iOS 17.5.1) from iCloud and then tried to log-in with my Apple-ID on my MacBook Pro.

Still does not work.

On my iPhone "Apple-ID", the MacBook Pro is listed again as a device (same as apple TV3 and iPad 2nd generation) even though I removed it before (see above).

How to resolve, so that I can sign-in with my Apple-ID on my MacBook Pro (incl. Mail)?

I appreciate any guidance. Thank you.

Screenshot: (note: all "internet accounts" have been deleted)